《先进功能材料力学(英文版)》由王彪所著。

This book is an attempt to tackle mainly the followingtwo proplems: (1) to analyze the effect of stress and deformation on the functionalproperties of the materials, and (2) to establish the quantitative models relatedwith the microstructural evolution. The general formulation will be developedfrom the detailed analyses of the separated examples.

1 Introduction

2 Basic Solutions of Elastic and Electric Fields of Piezoelectric Materials

 with Inclusions and Defects

 2.1 The Coupled Differential Equations of Elastic and Electric Fields in Piezoelectric Solids

2.1.1 Thermodynamic Framework

2.1.2 Linear Constitutive Equations

2.1.3 The Equation of Equlibrium

2.1.4 The Basic Equations of a Static Electric Field

2.1.5 Differential Equations for Piezoelectric Materials

 2.2 Boundary Conditions

 2.3 Solution Methods for Two-Dimensional Problems

2.3.1 The Stroh Formalism for Piezoelectric Materials

2.3.2 The Lekhnitskii Formalism for Piezoelectric Materials

2.3.3 Conformal Transformation of the Core Function

 2.4 Basic Solutions for Two-Dimensional Problems

2.4.1 Elliptical Cylindrical Inclusions in Piezoelectric Materials

2.4.2 Cracks

2.4.3 Dislocations and Line Charges

 2.5 Solution Methods for Three-Dimensional Problems

2.5.1 Eigenstrains and Equivalent Inclusion Method

2.5.2 Method of Fourier Integrals

2.5.3 Method of Green's Function

 2.6 Basic Solution for Three-Dimensional Problems

2.6.1 Ellipsoidal Inhomogeneous Inclusions

2.6.2 Flat Elliptical Cracks

2.6.3 Ellipsoidal Inhomogeneity Embedded in an Infinite Matrix when both Phases Undergo Eigenstrains

2.6.4 Green's Function

 2.7 Remarks

References

3 Micromechanics Models of Piezoelectric and Ferroelectrie Composites

 3.1 Background

 3.2 Some Definitions

 3.3 Effective Material Constants of Piezoelectric Composites

3.3.1 The Dilute Model

3.3.2 The Self-Consistent Model

3.3.3 The Mori-Tanaka Mean Field Model

3.3.4 The Differential Model

 3.4 Energy Formulation of Ferroelectric Composites

3.4.1 Elastic Strain Energy Density for Ferroelectric Composites

3.4.2 Intrinsic Free Energy Density for Ferroelectric Composites

3.4.3 Total Free Energy for Ferroelectric Composites with Spherical Inclusions

 3.5 Phase Diagrams

3.5.1 Total Free Energy for Ferroelectric Composites with

Spherical Inclusions and Equiaxed Strains

3.5.2 Phase Diagrams and Total Polarizations

 3.6 Remarks

 Appendix A: Radon Transform

 References

4 Determination of the Smallest Sizes of Ferroeleetric Nanodomains

 4.1 Introduction

 4.2 Electric Fields in Ferroelectric Thin Film

4.2.1 General Expression of Electric Field of Ferroelectric Domain

4.2.2 AFM-Induced Electric Field in Ferroelectric Thin Films

 4.3 Energy Expressions

4.3.1 Energy Expression for 180~ Domain in a Ferroelectric

 Film Covered with Top and Bottom Electrodes

4.3.2 Energy Expression for 180~ Domain in Ferroelectric

 Film Induced by an AFM Tip without the Top Electrode

 4.4 Driving Force and Evolution Equations of Domain Growth

 4.5 Stability Analysis

 4.6 Remarks

 Appendix B: Derivation of the Electric and Magnetic Field for a Growing 180° Domain

 References

5 Size and Surface Effects of Phase Transition on Nanoferroelectrie Materials

 5.1 Introduction and Overview of Ferroelectrics in Nanoscale Dimensions

5.1.1 Ferroelectric Thin Films in Nanoscale Dimensions

5.1.2 Ferroelectric Tunneling Junctions and Capacitors in Nanoscale Dimensions

5.1.3 Ferroelectric Multilayers in Nanoscale

5.1.4 Ferroelectric Nanowires and Nanotubes

5.1.5 Ferroelectric Nanograins or Nanoislands on Substrates

 5.2 Thermodynamic Modeling and Stability Analysis of Ferroelectric Systems

5.2.1 Background of the Thermodynamic Modeling for Ferroeleclrics

5.2.2 Electrostatics for Ferroelectrics

5.2.3 Thermodynamics of Ferroelectrics

5.2.4 Stability Analysis on Critical Properties of Ferroelectric Systems

 5.3 Ferroelectric Thin Films in Nanoscale

5.3.1 Thermodynamic Model for a Thick Ferroelectric Film

5.3.2 Size and Surface Effects on Ferroelectric Thin Films

5.3.3 The Evolution Equation and Stability of the Stationary States ..

5.3.4 Curie Temperature and Critical Thickness

5.3.5 Curie-Weiss Law of Ferroelectric Thin Film in Nanoscale

 5.4 Critical Properties of Ferroelectric Capacitors or Tunnel Junctions..

5.4.1 The Thermodynamic Potential of the Ferroelectric

Capacitors or Tunnel Junctions

5.4.2 The Evolution Equation and Stability of the Stationary States..

5.4.3 Curie Temperature of the Ferroelectric Capacitors or

Tunnel Junctions

5.4.4 Polarization as a Function of Thickness of the Ferroelectric

Capacitors or Tunnel Junctions

5.4.5 Critical Thickness of the Ferroelectric Capacitors or

Tunnel Junctions

5.4.6 Curie-Weiss Relation of the Ferroelectric Capacitors or

Tunnel Junctions .

 5.5 Ferroelectric Superlattices in Nanoscale

5.5.1 The Free Energy Functional ofFerroelectric Superlattices

5.5.2 The Phase Transition Temperature ofPTO/STO Superlattice.

5.5.3 Polarizafion and Critical Thickness ofPTO/STO Superlattice

5.5.4 The Curie-Weiss-Type Relation ofPTO/STO Superlattice

 5.6 Ferroelectric Nanowires and Nanotubes

5.6.1 Surface Tension ofFerroelectric Nanowires and Nanotubes.

5.6.2 Size and Surface Effects on Ferroelectric Nanowires

5.6.3 Ferroelectric Nanotubes

 5.7 Ferroelectric Nanograins or Nanoislands

5.7.1 Free Energy of Ferroelectric Nanograins or Nanoislands

5.7.2 Stability of the Ferroelectric State and Transition

Characteristics

5.7.3 Critical Properties of Nanograins or Nanoislands

 5.8 Remarks

 References

6 Strain Engineering: Ferroeleetrie Films on Compliant Substrates

 6.1 Background

 6.2 Manipulation of Phase Transition Behavior of Ferroelectric Thin

Films on Compliant Substrates

6.2.1 Free Energy Expressions

6.2.2 Evolution Equations

6.2.3 Manipulation of Ferroelectric Transition Temperature and Critical Thickness

6.2.4 Manipulation of the Order of Transition

 6.3 Piezoelectric Bending Response and Switching Behavior of

Ferroelectric Thin Film with Compliant Paraelectric Substrate

6.3.1 Model of Ferroelectric Thin Film with Compliant

Paraelectric Substrate and the Energy Expressions

6.3.2 Solution of the Evolution Equation

6.3.3 The Stationary and Relative Bending Displacements of the

Bilayer

6.3.4 Dynamic Piezoelectric and Bending Response of the

Bilayer Under a Cyclic Electric Field

6.3.5 Examples and Discussions

 6.4 Critical Thickness for Dislocation Generation in Piezoelectric Thin

Films on Substrate

6.4.1 Elastic and Electric Fields in a Piezoelectric Semi-Infinite

Space with a Dislocation

6.4.2 Critical Thickness for Dislocation Generation

6.4.3 Effect of Piezoelectric Behavior of the Materials on the

Critical Thickness for Dislocation Formation

 6.5 Critical Thickness of Dislocation Generation in Ferroelectdc

Thin Film on a Compliant Substrate

6.5.1 Mechanical Properties of the Problem

6.5.2 The Formation Energy and the Critical Thickness of Spontaneous Formation of Misfit Dislocation

 6.6 Remarks

 References

7 Derivation of the Landau-Ginzburg Expansion Coefficients

 7.1 Introduction

 7.2 Fundamental of the Landau-Devonshire Theory

7.2.1 The History of the Landau Free Energy Theory

7.2.2 The Thermodynamic Functions of the Dielectrics and Phase Transition

7.2.3 The Expansion of the Free Energy and Phase Transition

 7.3 Determination of Landau Free Energy Expansion Coefficients Based on Experimental Methods

7.3.1 The Experimental Observation of the Phase Transition Characteristics in Ferroelectrics

7.3.2 The Phenomenological Treatment of Devonshire Theory

7.3.3 The Elastic Gibbs Free Energy of PbTiO3 and Its Coefficients

7.3.4 The Determination of the Expansion Coefficients from

 the First-Principle Calculation Based on the Effective

 Hamiltonian Method

 7.4 Gradient Terms in the Landau-Devonshire-Ginzburg Free Energy Expansion

7.4.1 The Consideration of Spatial Non-uniform Distribution

 of the Order Parameters in the Landau Theory

7.4.2 The Critical Region and the Applicability of Landau

 Mean Field Theory

7.4.3 Determination of the Gradient Terms from the Lattice

Dynamic Theory

7.4.4 The Extrapolation Length and the Gradient Coefficient

 7.5 The Transverse Ising Model and Statistical Mechanics Approaches

7.5.1 Phase Transition from the Transverse Ising Model

7.5.2 Relationship of the Parameters Between Landau Theory

and the Transverse Ising Model

7.5.3 Determination of Landau-Ginzburg Free Energy Expansion

Coefficients from Statistical Mechanics

 7.6 Remarks

 References

8 Multiferroie Materials

 8.1 Background

 8.2 Coupling Mechanism of Multiferroic Materials

8.2.1 Single Phase Multiferroic Materials

8.2.2 Magnetoelectric Composites

 8.3 Theories of Magnetoeleclric Coupling Effect at Low Frequency

8.3.1 Energy Formulation for Multiferroic Composites

8.3.2 Phase Transition Behaviors in Layered Structures

8.3.3 Magnetoelectfic Coupling Coefficients in Layered Structures

 8.4 Magnetoelectric Coupling at Resonance Frequency

8.4.1 Magnetoelectric Coupling at Bending Modes

8.4.2 Magnetoelectfic Coupling at Electromechanical Resonance

8.4.3 Magnetoelectric Coupling at Ferromagnetic Resonance

 8.5 Remarks

 References

9 Dielectric Breakdown of Mieroeleetronie and Nanoeleetronie Devices.

 9.1 Introduction

 9.2 Basic Concepts

9.2.1 MOS Structure

9.2.2 Different Tunneling Modes

9.2.3 Dielectric Breakdown Modes

9.2.4 Defect Generation

9.2.5 Basic Statistical Concepts of Dielectric Breakdown

9.2.6 Stress Induced Leakage Current

9.2.7 Holes Generation

9.2.8 Energetics of Defects

 9.3 Mechanism Analysis of Tunneling Phenomena in Thin Oxide Film.

9.3.1 Self-consistent SchrSdinger's and Poisson's Equations

9.3.2 Transmission Coefficient

9.3.3 Tunneling Current Components

9.3.4 Microscopic Investigation of Defects from First-Principles Calculation

9.3.5 Manipulating Tunneling by Applied Strains

 9.4 Degradation Models in Gate Oxide Films

9.4.1 Anode Hole Injection Model

9.4.2 Thermochemical Model

9.4.3 Anode Hydrogen Release Model

9.4.4 Thermal Breakdown Model

9.4.5 Mechanical-Stress-Induced Breakdown Model

9.4.6 Remarks

 9.5 Statistical Models of Dielectric Breakdown

9.5.1 A Basic Statistical Model

9.5.2 A Three-Dimensional Statistical Model

9.5.3 Sphere and Cube Based Percolation Models

9.5.4 Combination of Percolation Model and Degradation Model

 9.6 Damage of Dielectric Breakdown in MOSFET

9.6.1 Lateral Propagation of Breakdown Spot

9.6.2 Dielectric Breakdown-Induced Epitaxy

9.6.3 Dielectric Breakdown-Induced Migration

9.6.4 Meltdown and Regrowth of Silicided Poly-Si Gate

9.6.5 Damage in Substrate

 9.7 Remarks

 References

 Index